Answer
$P = 643.09 \space Btu/h $
Work Step by Step
When $K = 0.27 K_C$, Subsitute $K_C = \frac{T_L}{T_H - T_L} $ into $K$
$K = (0.27) ( \frac{T_L}{T_H - T_L} )$
$K = (0.27) (\frac{294.26 K}{ 307.04 K - 294.26 K})$
$ K = 6.22 $
To find the power,
$P = \frac{W}{t} = \frac{Q_L/t}{k} $
$P =\frac{4000 Btu/h}{6.22} $
$P = 643.09 \space Btu/h $
